The polar coordinates of point P are given. Find all of its polar coordinates.
-$$\mathrm { P } = \left( 8,79 ^ { \circ } \right)$$
A) $\left( 8,79 ^ { \circ } + 360 n ^ { \circ } \right)$ or $\left( 8 , - 79 ^ { \circ } + ( 2 n + 1 ) 180 ^ { \circ } \right)$
B) $\left( 8,79 ^ { \circ } + 180 n ^ { \circ } \right)$ or $\left( - 8,79 ^ { \circ } + 180 n ^ { \circ } \right)$
C) $\left( 8,79 ^ { \circ } + 360 n ^ { \circ } \right)$ or $\left( - 8,79 ^ { \circ } + 360 n ^ { \circ } \right)$
D) $\left( 8,79 ^ { \circ } + 360 n ^ { \circ } \right)$ or $\left( - 8,79 ^ { \circ } + ( 2 n + 1 ) 180 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

In polar coordinates, a point can be represented in multiple ways. Adding $360^\circ$ to the angle gives a full rotation, bringing the point back to its original position, so $\left( 8,79^\circ + 360n^\circ \right)$ is correct. Changing the radius from $8$ to $-8$ flips the point across the origin, which requires adjusting the angle by $180^\circ$ to point in the opposite direction, hence $\left( -8,79^\circ + (2n+1)180^\circ \right)$ is also correct.

The Polar Coordinates of Point P Are Given P=(8,79∘)\mathrm { P } = \left( 8,79 ^ { \circ } \right)P=(8,79∘)

The Polar Coordinates of Point P Are Given $\mathrm { P } = \left( 8,79 ^ { \circ } \right)$